Question

If a random variable \(X\) has a probability mass function \(P(x) = \{\begin{array}{cc}kx^2, & \text{for }x = 1,2,3,4 \\ 0, & \text{otherwise}\end{array}\), then the mean of \(X\) is ...

• A. \(3.232\)
• B. \(2.221\)
• C. \(3.333\)
• D. \(2.222\)

Hint:

Find k from the total probability, then compute the sum of x P(x).

Answer 1

The Correct Option is C

Step 1: Find k
\(k(1+4+9+16) = 1\) gives \(30k = 1\), so \(k=\frac1{30}\).

Step 2: Mean
\(E(X) = \sum xP(x) = k(1+8+27+64) = \frac{100}{30}\).

Step 3: Value
\(\frac{100}{30} = 3.333\). Option (C).

Final Answer:
The mean is 3.333. \[ \boxed{\text{(C)}\ 3.333} \]